This invention relates generally to the determination of electromagnetic field characteristics and, in particular, to the determination of the electromagnetic field within a volume.
There are many problems in sensing and imaging which would benefit from a precise knowledge of the electromagnetic field at different points within a region or volume of interest. Examples include electromagnetic tracking, tomography, and remote sensing.
Existing methods of obtaining information about the electromagnetic field in a bulk/bounded volume are either slow, inaccurate, or restricted in terms of application. U.S. Pat. Nos. 4,737,794 to Jones; 4,314,251 to Raab; 4,394,831 and 4,287,809, both to Egli; 5,453,686 and European Patent Application No. 96304154, both to Anderson, each concern methods of measuring electromagnetic position and orientation in an aircraft cockpit, room in a building or other bounded volume. Implementation of these methods and, in particular, compensation for the distortion which arises, requires a definition of the field by moving sensors between discrete points in the volume. The methods are generally slow since the number of acquisition points is large. Also, all three components of the vector of magnetic induction are measured at each point, requiring precise mechanical equipment.
Other methods are restricted by application to optical/X-ray measurements in scattering media, or the methods are incomplete in that they are unable to restore/compute an accurate map of the electromagnetic field within a volume, including both the vector of magnetic induction and scalar potential. The method of U.S. Pat. No. 5,137,355 to Barbour et al., for example, involves computations of contributions of modeled scattered quasi-particles in the bulk, which are correlated to the flux intensity on the surface. The method is limited to infrared band and collimated measurements at discrete points using collimated sources or plurality of points of field illumination/irradiation.
The method of Huabei Jiang et al, Opt. Lett. 21, No. 20, employs measurement of the transmission of photon density waves (i.e., a modulated light beam). The number of illumination points is comparable with the number of sensors and computations of propagation matrix are iterative. The method of Jun Wu, J. Opt. Soc. Am. A14, No. 1 is based on a photon propagation in semi-infinite space medium with a single boundary based upon a step-like treatment of the properties of the medium on the boundary. The method of S. B. Colak et al,. Appl. Opt. 36, No. 1 is similar to that of Jun Wu, above, but uses a continuous-wave (CW) signal, and restores an intensity map with an empiric de-blurring function.
One application of electromagnetic position and orientation tracking is line-of-sight (LOS) tracking, which involves the measurement of a pilot""s look angle, as discussed in the patents to Jones and Egli referenced above. LOS trackers measure the position and orientation of sensing antennas relative to respective transmitting antennas. The technology is based on the generation and detection of AC electromagnetic fields, using a computer to calculate relative position and orientation from the sensed data using knowledge of field strength and direction throughout the environment.
Making reference to FIG. 1, the tracker""s transmitting antenna 102 floods the cockpit 104 with magnetic fields, and the signals sensed by helmet-mounted sensing antennas 106 are fed to an on-board computer where the sensor""s coordinates are calculated. Tracker transmitting and sensing antennas 102 and 104 each consist of three orthogonal coils of wire wound on a common bobbin, enabling the antennas to sense all three components of the electromagnetic field vector.
A difficulty with this technology is that AC electromagnetic fields induce eddy currents in conductors, of which there are many in a cockpit and other environments in which such systems are used. The induced currents in turn radiate magnetic fields that interfere or distort the intended fields, and ultimately cause errors in sensor coordinate calculations.
A precise determination or xe2x80x9cmappingxe2x80x9d of the electromagnetic field is therefore employed to measure field strength and/or direction within the volume prior to use of the tracking system. Such a process defines characteristics of the electromagnetic field inside the volume to create a map or a data table of these characteristics corresponding to the entire volume of interest. Measurements are traditionally performed using a precision fixture which translates mapping sensors to thousands of points 120 in the volume, as shown in FIG. 1. The electromagnetic field data collected during the mapping procedure are entered into the on-board computer, which uses it as a basis for sensor position and orientation computations. Changes to the environment mandate re-mapping of the volume.
A typical mapping fixture based upon existing technology may include: a) three-axis motors, precision drive screws, and carefully aligned three-axis mapping sensors; b) parts that have to be dismantled and reassembled in various configurations to reach all points of interest and to align the fixture; c) motor control electronics; and d) a computer with application software to control the movement of the mapper.
The process of using this type of fixture is tedious, prone to failure and error, and excessively time consuming. Excluding time for fixture installation and alignment, a typical procedure of this kind may take several days to two weeks per aircraft, and requires one or two qualified persons and about 600 pounds of equipment. Since a map of one aircraft cannot be applied accurately to another aircraft, the procedure must be repeated for every aircraft.
Other area of application of this invention are remote sensing and non-destructive measurements (see FIGS. 2 and 3), i.e., situations when points inside the volume of interest are inaccessible.
This invention enables the process of fast mapping (or defining characteristics within the volume) of the electromagnetic field by acquiring data from the surface bounding a volume of interest and solving the boundary value problem (BVP). Broadly, instead of measuring a plurality of the electromagnetic field components on a step-by-step basis at each point within a region of interest, only a single component of the field is measured on the surface bounding the region. In a preferred embodiment, the normal component of the electromagnetic induction or the normal to the surface derivative of the scalar potential is the measured quantity.
Since the amount of data to be collected is relatively small (one component at the surface instead of three components in an entire volume) and data acquisition does not require moving parts, the data can be collected in a very short time as compared to existing techniques. The acquired data forms the input to the boundary value problem, and the solution is, in fact, the scalar potential (or electromagnetic induction, or flux) of the electromagnetic field in the bulk.
In a preferred embodiment the solution to the BVP is based upon using Green""s functions, which can be computed independently and before data acquisition begins using knowledge of the physical process of propagation of the electromagnetic waves and geometry of the volume of interest. The necessary computations of Green""s functions or weight functions may take from minutes to days on existing computer hardware (depending on available hardware and required accuracy), but it only needs to be computed once for a given geometry and physical process, and the result does not depend on acquired data. Following this initial computation the functions may be applied repeatedly to new mapping data in a very direct and straightforward manner, taking from milliseconds to, at most, a few minutes to complete the solution (depending on required accuracy). As such, a single fixture may be used to map different types of environments, depending upon the application.
Another feature of the disclosed method is its ability to correct errors due to discretization, noise, truncation, or other numerical causes. The errors are detected, and then fed back into the process by treating the errors at each computed point as virtual sources of the electromagnetic field, then subtracting their contributions from the solution. Conveniently, the error reduction algorithm uses the same pre-computed Green""s functions.
These three important aspects of the invention, namely, surface single component data acquisition, the Green""s function based BVP solution, and error correction employing the treatment of errors as virtual sources, combine to produce a process of determining electromagnetic fields inside a volume that reduces to a few minutes what presently takes days to complete, or sometimes impossible. Data acquisition may be carried out either by moving sensors along the surface or, preferably, by fixing the position of several single axis or one-directional sensors on the surface bounding the volume. The latter does not require moving parts.
The technique is capable of determining different characteristics of the field such as the intensity of flux, scalar potential, or electromagnetic induction. The invention is applicable to numerous commercial products which would benefit from the mapping or definition of an electromagnetic field in a bounded volume. The invention is further applicable to situations when points inside the volume of interest are inaccessible, since the approach allows determining characteristics of t he electromagnetic field inside this volume by acquiring only the surface data. In addition to electromagnetic tracking systems such as LOS tracking, the methodology is directly applicable to electromagnetic motion capture systems, tomographic systems and devices (including optical, X-ray, magnetic), non-destructive electromagnetic measurements, and remote sensing (FIGS. 1-3).